Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations
 作者： Wei Qu,  Yong Liang 作者单位： 1State Key Laboratory of Quality Research in Chinese Medicines & Faculty of Information Technology, Macau University of Science and Technology2School of Mathematics and Statistics, Shaoguan University 刊名： Advances in Difference Equations, 2017, Vol.2017 (1), pp.1-11 来源数据库： Springer Nature Journal DOI： 10.1186/s13662-017-1150-1 关键词： Crank-Nicolson scheme;  tempered fractional diffusion equations;  unconditionally stable;  convergence;  variable coefficients; 原始语种摘要： Abstract(#br)A Crank-Nicolson scheme catering to solving initial-boundary value problems of a class of variable-coefficient tempered fractional diffusion equations is proposed. It is shown through theoretical analysis that the scheme is unconditionally stable and the convergence rate with respect to the space and time step is O ( h 2 + τ 2 ) $\mathcal{O}(h^{2} +\tau^{2})$ under a certain condition. Numerical experiments are provided to verify the effectiveness and accuracy of the scheme.

• convergence　汇合
• fractional　分级的
• tempered　回火
• coefficient　系数
• scheme　略图
• variable　变量
• class
• diffusion　扩散
• Crank　起重机